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2004-2005 Dominated convergence theorem involving small Riemann sums.
Ch. Rini Indrati, Peng Yee Lee
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Real Anal. Exchange 30(2): 783-794 (2004-2005).


We define two interval functions $U_\delta$ and $V_\delta$ using Riemann sums of Henstock integrable functions, as major and minor functions. Then we formulate two dominated convergence theorems for the Henstock integral in the $n$-dimensional space.


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Ch. Rini Indrati. Peng Yee Lee. "Dominated convergence theorem involving small Riemann sums.." Real Anal. Exchange 30 (2) 783 - 794, 2004-2005.


Published: 2004-2005
First available in Project Euclid: 15 October 2005

zbMATH: 1110.26007
MathSciNet: MR2177435

Primary: 26A39

Keywords: $\delta$-fine partition , $U_{\delta}$ , $V_{\delta}$ , Equi-Henstock integrability. , Functionally Small Riemann Sum , Henstock integral , Locally Small Riemann Sum , non-absolute partition , Uniformly Strong Lusin Condition

Rights: Copyright © 2004 Michigan State University Press

Vol.30 • No. 2 • 2004-2005
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